Narrow band lters. 1 Filters characteristics. I. Rodríguez and O. Lehmkuhl. January 8, FWHM or bandpass

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1 Narrow band lters I. Rodríguez and O. Lehmkuhl January 8, Filters characteristics The three most important parameters in a narrow band lter are the FWHM (or bandpass), the maximum transmittance and the out-of-band blocking. To understand each of these characteristics is important in order to adequately select the narrow band lter. Let's to explain each of them. FWHM or bandpass The technical term of Full-Width at Half-Maximum or FWHM is a simple measure of the width of a distribution. In astrophotography is used to describe a measurement of the width of an object in a picture, when that object does not have sharp edges. In the case of the image of a star in an astronomical photo, has a prole which is closer to a Gaussian curve, given mathematically by f(x) = exp( x2 2σ 2 ) (1) The above equation can be represented graphically as in gure 1 Figure 1: Representation of the FWHM of a gaussian distribution 1

2 Figure 2: Representation of the bandpass of a lter Figure 3: Cone light angle of incidence In a lter, the FWHM or the bandpass can be dened as the width measured at the half maximum transmission.bandwidth describes the size of a spectral segment. A bandwidth of 10nm indicates a range of 10nm of radiation. It is measured in [nm] and as can be observed is a band around the wavelenght of pass (see gure 2). The bandpas of a narrowband lter is a function of the light incidence angle. This angle can be easily evaluated from the focal radio of the scope by means of simple trigonometrics relationships. In the g 3, the cone of light is shown. It is the result of the light entering the scope and focussing at a point. The angle produced by the light cone can be calculated as: θ = tan 1 D 2F (2) where D is the scope diameter (apperture) and F is the focal length. If the focal ratio is f = F/D, thus the above equation can be expressed as: θ = tan 1 1 2f (3) 2

3 The bandpass in narrowband lters is a function of the incident light angle. The combination of a steep light cone and wide eld angles limits the use of narrowband ltes to slower systems 1. In this situation, the bandpass wavelenght of the lter shifts with increasing angle toward shorter wavelenghts. Thus, it can aects/reduces the eciency of the lter. The following formula can be used to determine the wavelength shift of a lter in collimated light with incident angles up to 15 degrees: λ θ = λ 0 [1 ( N e N f ) 2 sin 2 θ] 1 2 (4) where λ θ is the wavelength at the incident angle, λ 0 is the wavelength at normal incidence, N e is the refractive index of the external medium, N f is the refractive index of the lter and θ is the incidence angle. For fast telescopes (faster than f/4), lters narrower than 13nm will be degraded. For slower systems a narrower lter is recommended as it enhances the eect of the lter. 1.1 Maximum transmittance The ratio of the radiant power transmitted through a material to the incident radiant power. Transmittance is usually expressed as a percent. A lter with a 50% transmittance (at a specic wavelength) will absorb half of the light incident on it and allow half of it to pass through it. The higher transmittance of the lter at the pass wavelength (e.g. at 656.3nm for the case of an Hα lter), the better eciency obtained. 1.2 Out-of-band blocking The out-of-band blocking is the attenuation of the incidence radiation at wavelenght dierent than the pass wavelenght. It is important for a lter all the unwanted radiation, at all the wavelength other than the pass one at which transmittance should be maintained at a maximum.a good out-of-band blocking can allow to achieve very high signal to noise ratio (SNR) and high contrast, even with a bright moon nearby or under light polluted skies. 2 How to select the lter There are a lot of variety of lters for the dierent pass wavelength (Hα, [OIII], [SII]) in the market at dierent prices. The most known: Astrodon, Astronomik, Baader, etc. Manufacturers also oer dierent bandpass (6nm, 7nm, 10nm, 13nm, etc.). Thus, it can be a dicult decision for which lter to select. There 1 Slower systems is referred to system with focal ratios equal or greater than f/4 3

4 is not a unique answer, because it depends of your optical system and of course (maybe the most important) your budget. At the same bandpass, the higher transmittance the better. At the same transmittance, the narrower the bandpass the better. In both cases, SNR increase. Another think to take into account if you plan to buy not only the Hα lter but also the [SII] and [OIII] lters is that they should be parfocal, i.e. they all focus at the same point. This should eliminate the need for refocusing when you change of lter. 3 How to detect the halos source An usual problem when taking photos with lters (not always is the only cause of halos) is that sometimes appear non-desired halos around stars. These halos depend on the conguration used, but also they can be due to a bad performace of the antireection coating on the optical elements near the image. This condition is worst for fast systems. The dominant factor in these systems is the steep incidence angles. At high angles coatings have increased reection. With more reected light enanating from the optical surfaces, halos will appear. In fast systems even with high anti-reection coatings images will have halos. It is the limits of the physics. These conditions exist in all systems but are more pronounced in fast systems. The most important thing is to know which surface is the cause of these halos at the CCD. Hereafter we'll try to comment some useful steps to nd what cause them. For more information [1]. First step if your taking photos with dierent lters (says RGB or Ha [OIII] [SII]) is to detect if the halos are reproduced in the dierent images taken with dierent lters. This is important because if halos are produced by the three lters, then they are not dependent of the lter bandpass. In this case a good hypothesis is that there are reections. Secondly, we will calculate the halo size on the CCD. First measure the number of pixels that are contained in the halo diameter. To do this strech the histogram until the halo can be observed in the image. The halo size is: Halo diameter at the CCD = diameter in pixels pixel size (5) where the pixel size is in mm. If the photo has been taken in binning, says 2x2, then you have to multiply the pixel size by 2. We will nd the source of the reection. To do this, we must nd how far away from the CCD is the source of this reection. In a simmilar manner as you calculate the focal distance of your scope from the focal ratio and the diameter, you can calculate the distance from the CCD where the reection is produced. 4

5 Ref lectance distance = f halo diameter (6) In gure 4 each halo diameter is caused by a dierent reection, between the entrance window and the lter, between the entrance window and the chip, due to entrance window thickness. In all cases, each reection distance is twice the distance between the surfaces that cause the reection. In the gure it is not represented the cover of the chip that can also cause a reection. References [1] 5

6 Figure 4: Diagram of the dierent surfaces from the lter to the CCD chip 6